Local Density Estimation Procedure for Autoregressive Modeling of Point Process Data

We proposed a procedure to pre-process data used in a vector autoregressive (VAR) modeling of a temporal point process by using kernel density estimation. Vector autoregressive modeling of point-process data, for example, is being used for causality inference. The VAR model discretizes the timeline into small windows, and creates a time series by the presence of events in each window, and then models the presence of an event at the next time step by its history. The problem is that to get a longer history with high temporal resolution required a large number of windows, and thus, model parameters. We proposed the local density estimation procedure, which, instead of using the binary presence as the input to the model, performed kernel density estimation of the event history, and discretized the estimation to be used as the input. This allowed us to reduce the number of model parameters, especially in sparse data. Our experiment on a sparse Poisson process showed that this procedure vastly increases model prediction performance.